Discrete Linear Canonical Transform on Graphs: Uncertainty Principle and Sampling
arxiv(2024)
摘要
With an increasing influx of classical signal processing methodologies into
the field of graph signal processing, approaches grounded in discrete linear
canonical transform have found application in graph signals. In this paper, we
initially propose the uncertainty principle of the graph linear canonical
transform (GLCT), which is based on a class of graph signals maximally
concentrated in both vertex and graph spectral domains. Subsequently,
leveraging the uncertainty principle, we establish conditions for recovering
bandlimited signals of the GLCT from a subset of samples, thereby formulating
the sampling theory for the GLCT. We elucidate interesting connections between
the uncertainty principle and sampling. Further, by employing sampling set
selection and experimental design sampling strategies, we introduce optimal
sampling operators in the GLCT domain. Finally, we evaluate the performance of
our methods through simulations and numerical experiments across applications.
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